1.Easy
A rectangular section has width b = 240 mm and height h = 475 mm. Find its second moment of area Ibase about the axis along its bottom edge.
b = 240 mmh = 475 mm
Ibase = × 10⁶ mm⁴
Centroid & second moment of area worksheet with answers
2.Easy
A 240 mm × 150 mm plate has a circular hole of diameter 40 mm whose centre is 72 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 240 mmh = 150 mmd = 40 mmhole centre: x = 72 mm
x̄ = mm
3.Medium
A 150 mm × 300 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 210 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 150 mmh = 300 mmd = 50 mmhole centre: y = 210 mm
Ix = × 10⁶ mm⁴
4.Medium
A channel section lies with its open side up: a base plate 200 mm wide with two upright legs, 140 mm high overall. Base and legs are all 10 mm thick. Find the height ȳ of the centroid above the bottom edge.
b = 200 mmh = 140 mmt = 10 mm
ȳ = mm
5.Hard
A 120 mm × 300 mm plate has a rectangular cut-out 50 mm wide and 50 mm high, centred on the vertical centre line with its centre 90 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 120 mmh = 300 mmcut-out: 50 × 50 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
6.Hard
The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the bending stress σbottom at the bottom edge.
bf = 220 mmtf = 30 mmtw = 8 mmhw = 240 mmM = 10 kN·m
σbottom = MPa
Answer key
- 1. Ibase = 8574 × 10⁶ mm⁴
- 2. x̄ = 121.7 mm
- 3. Ix = 329.8 × 10⁶ mm⁴
- 4. ȳ = 44.57 mm
- 5. Ix = 259.8 × 10⁶ mm⁴
- 6. σbottom = 61 MPa
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